Transformation induced crack closure and fatigue life analysis of shape memory alloys using finite elements

Abstract

Fatigue crack propagation behavior of shape memory alloys is investigated using finite elements. Fatigue crack growth rate is numerically determined in terms of effective stress intensity factor range and maximum stress intensity factor. Finite element model of crack closure used is similar to that used by Kibey et al. [68] on plasticity induced crack closure in elastic-plastic materials with hardening. Before studying fatigue crack growth, fracture behavior of the material (such as size of phase transformation zone in cracked specimen, J-integral, stress intensity factor, etc.) is discussed. Stress distribution in transformation zone around the crack tip is solved analytically using HRR singularity field. A correlation between J-integral and stress intensity factor is checked. No plastic strain accumulation during cyclic loading is allowed in the material model used for the superelastic alloy, therefore the phase transformation is considered to be the only mechanism triggering crack closure. A detailed analysis is made to see effects of load ratio, initial crack length and crack propagation history on elastic and transformation strain energies during crack propagation. To estimate the fatigue life of a typical shape memory alloy, stress intensity factor in terms of final crack length and applied load is estimated by using an empirical formulation. Results obtained from this method are compared to analytical results in literature. Finally, service life of the material is calculated regarding all aspects of its fatigue behavior.